Modeling of Warm Dense Plasmas for the Determination of Transport Properties and Equation of State

Abstract

We present the results of research studying the properties of dense plasmas using the average atom model. The average atom model is a physically reasonable statistical representation of an atom in a plasma, and various forms of average atom models have been implemented over the past four decades. We developed a formalism using Green’s functions to construct an average atom electronic density that overcomes many of the numerical difficulties that plague other implementations. The code developed in this work includes a relativistic and nonrelativistic implementation. The average atom model, though in and of itself useful to describe the statistical properties of a dense plasma, also serves as an excellent starting point upon which additional models can be built. We demonstrate how the underlying average atom model implemented in the beginning of this work (Chapters 2 and 3) could be built upon to include more correlations between ions in the plasma. This is done through use of a pseudoatom model that incorporates information on the correlations between ions and electrons in the plasma on top of an average atom calculation. In Chapter 4 we use this model to extract a mean-force potential which allows us to get improved results for electrical conductivity, with especially significant results for the free-free contribution. In Chapter 5 we apply a molecular dynamics calculation along with the pseudoatom model to create a more physically informed structure factor for the ions in a plasma. In Chapter 6 we show that the average atom model provides a good ground state electron density for use in a time-dependent density functional theory calculation. These time-dependent calculations incorporate the dynamic response of the multi-electron average atom system to an external perturbation, and the results generated show good agreement with experiments. Overall the work in this dissertation collectively demonstrates the usefulness of the average atom model as both a means of determining thermodynamic properties of plasmas and as a starting point for building more complex models.